Question: Simplify the following expression: $ x = \dfrac{-4t + 5}{-7} + \dfrac{4}{3} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-4t + 5}{-7} \times \dfrac{3}{3} = \dfrac{-12t + 15}{-21} $ Multiply the second expression by $\dfrac{-7}{-7}$ $ \dfrac{4}{3} \times \dfrac{-7}{-7} = \dfrac{-28}{-21} $ Therefore $ x = \dfrac{-12t + 15}{-21} + \dfrac{-28}{-21} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-12t + 15 - 28}{-21} $ $x = \dfrac{-12t - 13}{-21}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{12t + 13}{21}$